Various types of sockets made of heat-resistant, electrically insulating material, such as cermaics and the like, are known; one socket is described, for example, in German Patent Publication DE-OS No. 32 36 462 to which U.S. Pat. No. 4,533,851 corresponds. Such sockets can accept voltages of more than 20 KV with good operating reliability and safety regarding electrical data; such voltages are necessary in order to re-ignite a high-pressure discharge lamp, for example after having been operated before, that is, to ignite the discharge lamp under hot conditions. It is necessary that the terminal ends for the supply voltage and for the high-voltage ignition pulses are spaced sufficiently apart and insulated from each other to prevent sparks or flash-over. Yet, it is also necessary that the high-voltage terminals are accessible so that the lamp and a lamp base can be readily inserted into the socket. Structures like the one described in the referenced U.S. Pat. No. 4,533,851, or corresponding German Publication No. 32 36 462, while entirely suitable from an electrical point of view, have been found to have high heat capacity due to their high mass. The lamp, which operates at high temperatures, transfers heat to the base and to the socket and this heat is not readily radiated; this is disadvantageous for operation of the lamp and, particularly, for operation of the lamp in a reflector of fixture. The base is quite large and if the lamp is to be inserted into a reflector, the resulting opening necessary in the reflector to permit introduction of the base of the lamp and also of the massive socket detracts from the light output since some of the light will not be reflected from the reflector but, rather, will be directed towards the lamp base and the lamp socket, contributing only to the undesirable heating thereof. The engagement surface of the lamp is located at the bottom of a collar accepting the socket bushings. The resulting construction is axially comparatively long; so that positioning of the lamp within the reflector at an accurately predetermined location in relation to its focal point is difficult.